Doggy Doors...What to do?

I did an audit yesterday and found out that a single doggy door was responsible for 1,300 CFM50 of air leakage (in an already-leaky house...total leakage of 5,300 CFM50 and only 2,200 square feet of conditioned floor area).

So, what to do about this doggy door? I could spent some time thinking of a clever way to address this, or do some research online, but I thought of y'all first, as the preeminent professionals.

Most pet flaps have some sort of positive closure, magnet or similar, and for the most part they work OK, although some air works its way around the flap's perimeter.

What I think happened here is that the blower door test pressure, which far exceeds natural pressure, overwhelmed the flap's magnet and it swung open, allowing an extra 1300 CFM. That should not occur under normal, non-blower-door test conditions.

Locating pet doors on a relatively sheltered wall of the house could help. I've been designing a two door doggie airlock in my head. It would be disguised as a bench (or banco in my neck of the woods), be heavily insulated, and vented to the exterior to disperse pulses of wind back to the outside of the house. If the vent could exhaust around a corner from the exterior flap that would be best, and it should have some kind of a flapper to reduce air coming in it. Or build the whole thing on the outside as a tunnel with exterior door at the end and vents both sides.

I recently had a similar situation, only the doggy door was big enough for an adolescent to crawl through. When I told my client she should consider replacing the door, she waxed nostalgic about the happy times when her dog and children would chase each other through the door. She made it clear she'd never replace the thing. I still haven't done any work for her.

Another trick I've seen is to dedicate the bottom half of a cabinet as a vestibule/mud-room with a second air-lock flapper like Peter suggests. Obviously you'ed need to design some people access to clean it out occasionally, but I agree with Glen re. the other 4000 cfm.